Polyurethane nanocomposites

ABSTRACT

Polyurethane nanocomposites are provided which include a polyurethane and surface modified silica nanoparticles covalently bound into the polyurethane. High loadings in excess of 30% may be achieved. In some embodiments, the silica nanoparticles are covalently bound to the polyurethane polymer through a linkage derived from a surface-modifying compound comprising a silane functional group and a polyol segment. In some embodiments the polyurethane nanocomposite may be provided as a tape or film. In addition, precursors for a polyurethane nanocomposites are provided comprising: a first polyol and surface modified silica nanoparticles dispersed within the first polyol. In some embodiments, the silica nanoparticles are surface-modified by reaction with a surface-modifying compound comprising a silane functional group and a polyol segment derived from a second polyol, which may be the same or different from the first polyol.

CROSS REFERENCE TO RELATED APPLICATION

This application is a divisional of U.S. application Ser. No.12/978,699, filed Dec. 27, 2010, now pending, which claims the benefitof U.S. Provisional Patent Application No. 61/290,754, filed Dec. 29,2009, the disclosure of which is incorporated by reference herein in itsentirety.

FIELD OF THE DISCLOSURE

This disclosure relates to polyurethane nanocomposites which include apolyurethane and surface modified silica nanoparticles are covalentlybound into the elastomeric polyurethane.

SUMMARY OF THE DISCLOSURE

Briefly, the present disclosure provides a polyurethane nanocompositecomprising: a) a polyurethane polymer, and b) surface modified silicananoparticles dispersed within and covalently bound to the polyurethanepolymer. Typically, the polyurethane nanocomposite according to claim 1having a silica content of greater than 12% by weight, more typicallygreater than 18% by weight, and more typically greater than 30% byweight. In some embodiments, the silica nanoparticles are covalentlybound to the polyurethane polymer through a linkage derived from asurface-modifying compound comprising a silane functional group and apolyol segment. Typically, the polyol segment has a molecular weight ofat least 500. In some embodiments, the surface modified silicananoparticles have a number average particle size of between 5 and 500nanometers (nm) and optionally exhibit a multimodal particle sizedistribution. In some embodiments, the surface modified silicananoparticles are also surface-modified by reaction with a secondsurface-modifying compound comprising a silane functional group andhaving a molecular weight of less than 800, more typically less than500, and more typically less than 350. Typically the secondsurface-modifying compound comprises no polyol segment. In someembodiments, the polyurethane comprises an acrylate component capable ofradiation-induced crosslinking. In some embodiments the polyurethanenanocomposite may be provided as a tape or film.

In another aspect, the present disclosure provides a precursor for apolyurethane nanocomposite comprising: a) a first polyol, and b) surfacemodified silica nanoparticles dispersed within the first polyol.Typically, the precursor for a polyurethane nanocomposite has a silicacontent of greater than 18% by weight, more typically greater than 30%by weight, and more typically greater than 50% by weight. In someembodiments, the silica nanoparticles are surface-modified by reactionwith a surface-modifying compound comprising a silane functional groupand a polyol segment derived from a second polyol. Typically, the polyolsegment has a molecular weight of at least 500 and more typically atleast 800. In some embodiments, at least one second polyol is the samepolyol as at least one first polyol. In some embodiments, the secondpolyol is essentially the same polyol as the first polyol. In someembodiments, the surface modified silica nanoparticles have a numberaverage particle size of between 5 and 500 nanometers (nm) andoptionally exhibit a multimodal particle size distribution. In someembodiments, the surface modified silica nanoparticles are alsosurface-modified by reaction with a second surface-modifying compoundcomprising a silane functional group and having a molecular weight ofless than 800, more typically less than 500, and more typically lessthan 350. Typically the second surface-modifying compound comprises nopolyol segment. In some embodiments, the polyurethane comprises anacrylate component capable of radiation-induced crosslinking.

In another aspect, the present disclosure provides a method comprisingthe steps of: a) mixing precursor for a polyurethane nanocomposite witha isocyanate polyurethane precursor to make a reactive mixture; b)applying the reactive mixture to a substrate; and c) curing the reactivemixture.

DETAILED DESCRIPTION

The present disclosure provides polyurethane nanocomposites whereinsurface modified silica nanoparticles are covalently bound into theelastomeric polyurethane backbone. The surface treatment allows thenanosilica to be well dispersed and bound in the polyurethane matrix.The surface treatment enables unusually high loadings of nanosilica, insome embodiments without a large increase in viscosity. The surfacetreatment enables bulk polymerization of the polyurethane nanocomposite.

The present disclosure additionally provides films comprising thepolyurethane nanocomposites of the present disclosure. The presentdisclosure additionally provides methods of using such films as erosionresistant covering layers or coatings, such as may be used on leadingedges of helicopter rotor blades, wind turbine blades, fixed wingaircraft, or the like.

Any suitable polyurethane may be used in the practice of the presentdisclosure. In some embodiments, the polyurethane comprises an acrylatecomponent. In some embodiments, the polyurethane comprises an acrylatecomponent capable of crosslinking. In some embodiments, the polyurethanecomprises an acrylate component capable of radiation-inducedcrosslinking with application of ebeam or EM radiation such as UVradiation. In some embodiments, the polyurethane comprises no acrylatecomponent. In some embodiments, the polyurethane is a mixedpolyurethane/polyurea. In some embodiments, the polyurethane is not apolyurea nor a mixed polyurethane/polyurea.

Any suitable silica nanoparticles may be used in the practice of thepresent disclosure. In some embodiments, silicas useful in manufactureof the materials of this disclosure are commercially available fromNalco Chemical Co. (Naperville, Ill.) under the product designationNALCO COLLOIDAL SILICAS. Such silicas may include NALCO products 1040,1042, 1050, 1060, 2327 and 2329. In some embodiments the surfacemodified silica nanoparticles incorporate silane compounds. In someembodiments the silica nanoparticles are not clay nanosilicates. In someembodiments, the silica nanoparticles have a number average particlesize of between 5 and 500 nanometers (nm), and in some embodiments,between 10 and 200 nm. In some embodiments, the silica particles usedexhibit a multimodal size distribution as described in U.S. ProvisionalPat. App. 61/303,406, the disclosure of which is incorporated herein byreference. In addition the disclosure of U.S. Pat. No. 5,648,407 isincorporated herein by reference.

Any suitable amount of silica may be included in the polyurethanenanocomposites of the present disclosure. In some embodiments, thesilica content is between 1% and 90% by weight. In some embodiments, thesilica content is between 1% and 65% by weight. In some embodiments, thesilica content is between 1% and 50% by weight. In some embodiments, thesilica content is between 3% and 35% by weight. In some embodi-ments,the silica content is between 3% and 90% by weight. In some embodiments,the silica content is between 3% and 65% by weight. In some embodiments,the silica content is between 3% and 50% by weight. In some embodiments,the silica content is between 5% and 35% by weight. In some embodiments,the silica content is between 5% and 90% by weight. In some embodiments,the silica content is between 5% and 65% by weight. In some embodiments,the silica content is between 5% and 50% by weight. In some embodiments,the silica content is between 8% and 35% by weight. In some embodiments,the silica content is between 8% and 90% by weight. In some embodiments,the silica content is between 8% and 65% by weight. In some embodiments,the silica content is between 8% and 50% by weight. In some embodiments,the silica content is between 8% and 35% by weight. In some embodiments,the silica content is between 12% and 90% by weight. In someembodi-ments, the silica content is between 12% and 65% by weight. Insome embodiments, the silica content is between 12% and 50% by weight.In some embodiments, the silica content is between 15% and 35% byweight. In some embodiments, the silica content is between 15% and 90%by weight. In some embodiments, the silica content is between 15% and65% by weight. In some embodiments, the silica content is between 15%and 50% by weight. In some embodiments, the silica content is between15% and 35% by weight. In some embodiments, the silica content isbetween 18% and 90% by weight. In some embodiments, the silica contentis between 18% and 65% by weight. In some embodiments, the silicacontent is between 18% and 50% by weight. In some embodiments, thesilica content is between 18% and 35% by weight. In some embodiments,the silica content is between 21% and 90% by weight. In someembodiments, the silica content is between 21% and 65% by weight. Insome embodiments, the silica content is between 21% and 50% by weight.In some embodiments, the silica content is between 21% and 35% byweight. In some embodiments, the silica content is between 25% and 90%by weight. In some embodiments, the silica content is between 25% and65% by weight. In some embodiments, the silica content is between 25%and 50% by weight. In some embodiments, the silica content is between25% and 35% by weight. In some embodiments, the silica content isbetween 30% and 90% by weight. In some embodiments, the silica contentis between 30% and 65% by weight. In some embodiments, the silicacontent is between 30% and 50% by weight. In some embodiments, thesilica content is between 30% and 35% by weight.

The silica nanoparticles may be surface modified by reaction withsurface-modifying compounds having one or more functional groups capableof covalently bonding to silica and one or more functional groupscapable of incorporation into a polyurethane polymer, thus providingcovalent bonding of the silica particles to the polyurethane polymer.Most typically, the functional groups capable of covalently bonding tosilica are silane groups. Most typically, the functional groups capableof incorporation into a polyurethane polymer are hydroxy groups, but mayalso be amine groups. In some embodiments, the surface-modifyingcompound additionally aids in dispersal of the silica nanoparticles inone component of the polyurethane prior to polymerization, typically thepolyol component. In some embodiments, the surface-modifying compound isa polyol comprising a silane group. In some embodiments, thesurface-modifying compound is a polyol to which a silane group is addedby reaction with a compound comprising a silane (or silane-generating)group and an isocyanate group. The polyol that forms a part of thesurface-modifying compound may be the same or different as a polyol usedin the polyurethane. In some embodiments, the polyol that forms a partof the surface-modifying compound is different from the polyol used inthe polyurethane. In some embodiments, at least one polyol that forms apart of the surface-modifying compound is the same as at least onepolyol used in the polyurethane. In some embodiments, the polyol orpolyols that form a part of the surface-modifying compound are the sameas at least some of the polyols used in the polyurethane. In someembodiments, the polyol or polyols used in the polyurethane are the sameas at least some of the polyols that form a part of thesurface-modifying compound. In some embodiments, the polyol or polyolsthat form a part of the surface-modifying compound are the same as thepolyol or polyols used in the polyurethane. In some embodiments, thepolyol that forms a part of the surface-modifying compound has a MW ofat least 100, more typically at least 200, more typically at least 500,and most typically at least 800. In some embodiments, an additionalsilane may be added to occupy additional binding sites on the silicaparticle. In some such embodiments, the additional silane may have amolecular weight of less than 800, more typically less than 500, moretypically less than 350, and more typically less than 250. In some suchembodiments, the additional silane comprises no polyol segment.

In various embodiments, the polyurethane nanocomposite materials may beapplied as a sheet, tape, boot, co-curable film layer, or a spray. Insome embodiments, the polyurethane nanocomposite materials may beapplied as a reactive mixture by mixing a the polyol polyurethaneprecursor having dispersed therein surface modified silica nanoparticleswith a isocyanate polyurethane precursor and applying by spraying,brushing, immersion or the like, followed by cure. In some embodiments,cured polyurethane nanocomposite materials may be applied in the form ofsheets, tapes, boots, or the like, with or without adhesive layers suchas pressure sensitive adhesives or curable adhesives. In someembodiments, the polyurethane nanocomposite may be used as erosionresistant covering layers or coatings. In some embodiments, thepolyurethane nanocomposite may be used as erosion resistant coveringlayers or coatings on leading edges of helicopter rotor blades, windturbine blades or fixed wing aircraft.

Objects and advantages of this disclosure are further illustrated by thefollowing examples, but the particular materials and amounts thereofrecited in these examples, as well as other conditions and details,should not be construed to unduly limit this disclosure.

EXAMPLES

Unless otherwise noted, all reagents were obtained or are available fromSigma-Aldrich Company, St. Louis, Mo., or may be synthesized by knownmethods. Unless otherwise reported, all ratios are by weight percent.

The following abbreviations are used to describe the examples:

° F.: Degrees Fahrenheit

° C.: Degrees Centigrade

mil: 10⁻³ inches

μm: micrometers

mm: millimeters

cm: centimeters

kg kilograms

kPa: kilopascals

psi: pounds per square inch

mg: milligrams

BDO refers to 1,4-butanediol, obtained from Alfa Aesar, Ward Hill, Mass.

DBTDL refers to dibutyltin dilaurate, obtained under the tradedesignation “DABCO T-12” from Air Products & Chemicals, Inc., Allentown,Pa.

IPDI refers to isophorone diisocyanate, obtained under the tradedesignation “VESTANAT IPDI” from Evonik Industries, Essen, Germany.

N2329 refers to an aqueous colloidal silica sol having an averageparticle size of 70-150 nm, received at 40.0% solids as determined bydrying in a oven at 150° C. for 30 minutes, obtained under the tradedesignation “NALCO 2329” from Nalco Company, Naperville, Ill.

PPT 8542HS refers to a polyurethane protective tape, obtained under thetrade designation “PPT 8542HS” from 3M Company, St. Paul, Minn.

PPT 8663 MB HS refers to a polyurethane protective tape, obtained underthe trade designation “PPT 8663MB HS” from 3M Company.

PPT 8671HS refers to a polyurethane protective tape, obtained under thetrade designation “PPT 8671HS” from 3M Company.

PTMEG refers to polytetramethylene ether glycol, having an averagemolecular weight of 1,000, obtained under the trade designation“TERATHANE 1000” from Invista S. ar. L., Wichita, Kans.

TEPS refers to n-triethoxypropylsilane, obtained from Sigma-AldrichCompany, St. Louis, Mo.

TESPI refers to 3-triethoxysilylpropyylisocyanate, obtained fromSigma-Aldrich Company.

TONE 2221 refers to a low-viscosity, linear polycaprolactone polyol,obtained under the trade designation “TONE 2221” from Dow ChemicalCompany, Midland, Mich.

TX10693 refers to an aqueous 90 nm silica sol, received at 32.5% solidsas determined by drying in a oven at 150° C. for 30 min, obtained underthe trade designation “TX10693” from Nalco Company, Naperville, Ill.

Thermogravimetric Analysis (TGA)

The silica content of the following silica-silane dispersions wasmeasured by TGA. A sample of approximately 20 mg of the dispersion wasplaced in a platinum TGA pan. The pan was loaded into athermogravimetric analyzer, model “Q500” from TA Instruments, Inc., NewCastle, Del., and ramped from 30° C. to 900° C. at a rate of 20°C./minute in an air purge. The weight percent of incombustible materialremaining is reported as the weight percent of total silica in thesilica-silane dispersion.

Silica-Silane Dispersion:

80 grams PTMEG was dissolved in 35 grams dry ethyl acetate at 70° F.(21.1° C.), to which 9.9 grams TESPI was slowly added. Four drops ofDBTDL was then added and the temperature kept below 40° C. whilecontinuing to stir the mixture for 16 hours. Residual ethyl acetate wasthen removed by vacuum distillation using a Buchi rotoevaporator set inan oil bath at 65° C. The silane equivalent weight of the mixture wascalculated to be 2250 g/mol. A pre-mix was then prepared by mixing 57.1grams of the silane mixture with 1,500 grams 1-methoxy-2-propanol and1.75 grams TEPS.

750 grams TX10693 was added to a 3-necked flask equipped with overheadstirrer, thermometer and condenser. While stirring, the premix wasslowly added over a period of 10 minutes and the mixture held between90-95° C. for 20 hours. After cooling the mixture was poured into analuminum foil pan and dried at 70° F. (21.1° C.) for 48 hours. Thesilica content of the resultant white silica-silane powder wasdetermined to be 85.5% by weight with TGA.

290 grams of the dried silica-silane powder was dispersed in 1,000 gramsof a 50:50 by weight acetone:tetrahydrofuran mixture for 90 seconds at70° F. (21.1° C.) using a high speed shear mixer set at 75% power, model“L4R”, obtained from Silverson Machines, Inc., East Longmeadow, Mass.After standing for 10 minutes, the dispersion was filtered through a 100μm nylon mesh, obtained under the trade designation “SPECTRA MESH 100 μmWOVEN FILTER” from Spectrum Laboratories, Inc., Rancho Domenguez, Calif.The silica-silane content of the dispersion was measured and found to be23.5% by weight by drying in an oven at 150° C. for 30 minutes.

1,000 grams of the silica-silane dispersion was mixed with 340 gramsPTMEG then stripped in the Buchi rotoevaporator for approximately 90minutes at 65° C., then for 30 minutes at 120° C. The silica % solidswas determined to be 39.0% by weight as measured by TGA.

Polyurethane Films:

Examples of the polyurethane film of the present disclosure, andcomparative formulations, were prepared as follows according to thecompositions listed in Table 1. PTMEG, the silica-silane dispersion, andBDO were mixed in a 50 ml. polyethylene beaker then dried in a vacuumoven for 3 hours at 70° C. and 0.97 atmospheres pressure (98.3 kPa) toremove any traces of water. IPDI was added, followed by DBTDL, mixeduntil homogeneous, then cast to a thickness of 12 mil (304.8 μm) betweentwo 3-mil (7.26 μm) thick polyethylene release liners and cured for 2hours at 70° C. The polyethylene liners were removed from the resultantpolyurethane film, silicone coated paper liners were applied, and thefilm repressed to 20 mil (508 μm) in a hot press, model number“50-2424-2TM” from Wabash Metal Products, Inc., Wabash, Ind., at 120° C.

TABLE 1 Silica-Silane Dispersion PTMEG BDO IPDI Silica Sample (g) (g)(g) (g) DBTDL (g) (wt %) Comp. A 0 15.0 0.60 5.01 0.10 0 Comp. B 0 14.00.80 5.29 0.10 0 Comp. C 0 13.5 1.31 6.48 0.13 0 Comp. D 0 13.0 1.506.85 0.13 0 Ex. 1 12.0 8.0 0.60 5.23 0.13 18% Ex. 2 20.0 0 0.20 3.280.12 33%

Sand Erosion Test:

A 3 by 2.67 inch (7.62 by 6.78 cm) sample of a polyurethane filmprepared above was laminated to an adhesive transfer film, obtainedunder the trade designation “965 Adhesive Transfer Film”, from 3MCompany, and applied to a 3 by 2.67 inch (7.62 by 6.78 cm) aluminumpanel. After recording the initial mass, the panel was then attached toan aluminum plate set 3 inches (7.62 cm), and at an angle of 30 degrees,to a sand blast gun, model number “SBC 420”, from Altas HandlingSystems, LLC. Two kg of aluminum oxide, obtained under the tradedesignation “46 GRIT BLAST MEDIA” from Grainger, Lake Forest, Ill., wasfired at the test sample at a pressure of 70 psi (482.6 kPa) forapproximately 2 minutes, after which the panel was removed andreweighed. Each sample was tested four times. The cumulative masseroded, and the corresponding cumulative volume eroded (based on asilica density of 2.1 grams/cm³), are reported in Table 2.

TABLE 2 Calculated Cumulated Mass Cumulative Volume Sample DensityEroded (mg) Eroded (cm³) Comparative A 1.1 18.2 0.063 Comparative B 1.116.2 0.059 Comparative C 1.1 21.6 0.071 Comparative D 1.1 31.1 0.095Example 1 1.28 18.5 0.053 Example 2 1.43 14.3 0.036 PPT 8542HS* 1.1 32.70.110 PPT 8663MB HS* 1.1 >93.1 0.240 Sample eroded through PPT 8671HS1.1 85.2 0.243 *Average of 2 samples

As evident in the sand erosion results, the addition of thesurface-modified nanosilica into the polyurethane formulation results inless volume loss compared to samples without surface-modifiednanosilica. Because it loses less volume, it will take more erodent towear through a sample containing surface-modified nanosilica, resultingin a film or coating with a longer in-service life.

Example 3

A further silica-silane dispersion was prepared as follows.

-   A. 80 grams of Tone 2221 Polyol (DOW Chemical) was placed in 25    grams of ethyl acetate and mixed well. A magnetic stir bar was added    and while stirring at room temperature, 9.9 grams of    3-triethoysilylpropylisocyanate was slowly added followed by 4 drops    of tin(di-n-butyldilaurate) (Alfa Aesar Lot FO9N01). The initial    exotherm was controlled by use of a water bath. The solution was    then stirred overnight and ethyl acetate was removed using a Buchi    rotovap with an oil bath set at 60-65° C. The silane equivalent    weight of the mixture was calculated to be 2250 g/mol.-   B. 150 grams of an aqueous solution of ion exchanged Nalco 2329    colloidal silica (Lot BP6C0673A2, 40% silica by weight measured by    drying in an oven at 150° C. for 30 minutes) was placed in a 3    necked flask equipped with overhead stirrer, thermo watch,    thermometer and condenser. While stirring at room temperature, 75    grams of 1-methoxy-2-propanol was added, followed quickly by enough    concentrated aqueous ammonium hydroxide to quickly bring the pH to    between 9-9.5. When solution remained homogeneous and fluid, a    premix of 155 grams of methoxypropanol, 13.2 grams of the silane    mixture prepared in A and 0.4 grams of triethoxypropylsilane was    added and the solution reacted 90-95° C. for 20 hours. The resulting    solution was poured into a foil pan and air dried at room    temperature to a white powder. Silica residue of the particle was    determined by TGA to be 81.0%.-   C. 18 grams of the material prepared in B was added to 50 grams of    acetone and high shear mixed using a Silverston (¾ speed for one    minute), then filtered through a 53u nylon mesh. Measured (by drying    in an oven at 150° C. for 30 minutes) silica/silane solids were    27.5% and silica solids were calculated to be 22.2%.-   D. 85 grams of the material prepared in C were placed in 35grams of    Tone 2221, mixed well and then stripped using a Buchi rotovap and an    oil bath set at 65° C. to remove volatiles. Final silica solids were    34.7% by weight as measured by TGA.

The silica-silane dispersion of Example 3 may be used as discussedabove.

Various modifications and alterations of this disclosure will becomeapparent to those skilled in the art without departing from the scopeand principles of this disclosure, and it should be understood that thisdisclosure is not to be unduly limited to the illustrative embodimentsset forth hereinabove.

We claim:
 1. A method comprising the steps of: a) mixing precursor for apolyurethane nanocomposite with an isocyanate polyurethane precursor tomake a reactive mixture; b) applying the reactive mixture to asubstrate; and c) curing the reactive mixture; wherein the precursor fora polyurethane nanocomposite comprises: x) a first polyol, and y)surface modified silica nanoparticles dispersed within the first polyol,where said nanoparticles are surface-modified by reaction with asurface-modifying compound comprising a second polyol to which a silanegroup is added by reaction with a compound comprising a silane orsilane-generating group and an isocyanate group.
 2. The method accordingto claim 1 wherein the precursor for a polyurethane nanocomposite has asilica content of greater than 18% by weight.
 3. The method according toclaim 1 wherein the precursor for a polyurethane nanocomposite has asilica content of greater than 30% by weight.
 4. The method according toclaim 1 wherein the precursor for a polyurethane nanocomposite has asilica content of greater than 50% by weight.
 5. The method according toclaim 1 wherein the silica nanoparticles are surface-modified byreaction with a surface-modifying compound comprising a silanefunctional group and a polyol segment derived from a second polyol. 6.The method according to claim 1 wherein the precursor for a polyurethanenanocomposite wherein the second polyol has a molecular weight of atleast
 500. 7. The method according to claim 1 wherein at least onesecond polyol is the same polyol as at least one first polyol.
 8. Themethod according to claim 1 wherein the second polyol is essentially thesame polyol as the first polyol.
 9. The method according to claim 1wherein the surface modified silica nanoparticles have a number averageparticle size of between 5 and 500 nanometers (nm).
 10. The methodaccording to claim 1 wherein the surface modified silica nanoparticlesexhibit a multimodal particle size distribution.
 12. The methodaccording to claim 1 wherein the surface modified silica nanoparticlesare surface-modified by reaction with a second surface-modifyingcompound comprising a silane functional group and having a molecularweight of less than
 350. 13. The method according to claim 12 whereinsaid second surface-modifying compound comprises no polyol segment. 14.The method according to claim 1 wherein said polyurethane comprises anacrylate component capable of radiation-induced crosslinking.
 15. Themethod according to claim 4 wherein the silica nanoparticles aresurface-modified by reaction with a surface-modifying compoundcomprising a silane functional group and a polyol segment derived from asecond polyol.
 16. The method according to claim 4 wherein the precursorfor a polyurethane nanocomposite wherein the second polyol has amolecular weight of at least
 500. 17. The method according to claim 4wherein at least one second polyol is the same polyol as at least onefirst polyol.
 18. The method according to claim 4 wherein the secondpolyol is essentially the same polyol as the first polyol.
 19. Themethod according to claim 4 wherein the surface modified silicananoparticles have a number average particle size of between 5 and 500nanometers (nm).
 20. The method according to claim 4 wherein the surfacemodified silica nanoparticles exhibit a multimodal particle sizedistribution.